Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues n/a

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Spectral parameter

$R= 29.3175625852$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.327606300
4 0.5
5 -0.447213595
6 0.938759418
7 0.372929500
8 0.353553390
9 0.762538489
10 -0.316227766
11 1.582219112
12 0.663803150
13 -0.887836633
14 0.263700978
15 -0.593723587
16 0.250000000
17 0.515691114
18 0.539196137
19 0.303805542
20 -0.223606797
21 0.495103554
22 1.118797864
23 0.147493213
24 0.469379709
25 0.200000000
26 -0.627795304
27 -0.315255397
28 0.186464750
29 1.559085253
30 -0.419825974
31 0.297822594
32 0.176776695
33 2.100564063
34 0.364648684
35 -0.166779142
36 0.381269244
37 -1.065625268
38 0.214822959
39 -1.178697509
40 -0.158113883
41 0.548580226
42 0.350091080
43 0.165825959
44 0.791109556
45 -0.341017579
46 0.104293451
47 0.383392167
48 0.331901575
49 -0.860923587
50 0.141421356
51 0.684634772
52 -0.443918316
53 -1.402670906
54 -0.222919229
55 -0.707589898
56 0.131850489
57 0.403334152
58 1.102439755
59 1.888688206
60 -0.296861793
61 -0.594906502
62 0.210592376
63 0.284373097
64 0.125000000
65 0.397052613
66 1.485323093
67 0.784948547
68 0.257845557
69 0.195812919
70 -0.117930662
71 1.454793476
72 0.269598068
73 1.320018968
74 -0.753510853
75 0.265521260
76 0.151902771
77 0.590056182
78 -0.833465001
79 0.0354547236
80 -0.111803398
81 -1.181073541
82 0.387904798
83 -1.461679309
84 0.247551777
85 -0.230624077
86 0.117256660
87 2.069851406
88 0.559398932
89 0.389809151
90 -0.241135843
91 -0.331100472
92 0.0737466066
93 0.395391153
94 0.271099201
95 -0.135865969
96 0.234689854
97 1.347473042
98 -0.608764907
99 1.206502973
100 0.100000000
101 0.518148929
102 0.484109890
103 1.548132265
104 -0.313897652
105 -0.221417040
106 -0.991838109
107 1.698444062
108 -0.157627698
109 -1.123067314
110 -0.500341615
111 -1.414730820
112 0.0932323750
113 -0.136451390
114 0.285200314
115 -0.0659609702
116 0.779542626
117 -0.677009605
118 1.335504238
119 0.192316429
120 -0.209912987
121 1.503417321
122 -0.420662422
123 0.728298565
124 0.148911297
125 -0.0894427190
126 0.201082145
127 -0.846440012
128 0.0883883476
129 0.220151588
130 0.280758595
131 0.300218595
132 1.050282031
133 0.113298049
134 0.555042440
135 0.140986499
136 0.182324342
137 0.224060333
138 0.138460643
139 -1.555446398
140 -0.0833895712
141 0.508993857
142 1.028694332
143 -1.404752091
144 0.190634622
145 -0.697244122
146 0.933394363
147 -1.142967578
148 -0.532812634
149 1.269943841
150 0.187751883
151 -1.907810231
152 0.107411479
153 0.393234320
154 0.417232728
155 -0.133190313
156 -0.589348754
157 -0.953374128
158 0.0250702755
159 -1.862194733
160 -0.0790569415
161 0.0550045728
162 -0.835145110
163 0.627929858
164 0.274290113
165 -0.939400807
166 -1.033563351
167 1.568714205
168 0.175045540
169 -0.211746051
170 -0.163075849
171 0.231663467
172 0.0829129796
173 -0.695474598
174 1.463605965
175 0.0745859000
176 0.395554778
177 2.507434267
178 0.275636694
179 0.211633830
180 -0.170508789
181 -1.786002071
182 -0.234123389
183 -0.789801537
184 0.0521467256
185 0.476562107
186 0.279583765
187 0.815934792
188 0.191696083
189 -0.117568892
190 -0.0960717480
191 1.250251896
192 0.165950787
193 0.452878351
194 0.952807325
195 0.527129551
196 -0.430461793
197 1.073157254
198 0.853126433
199 0.419544923
200 0.0707106781
201 1.042088660
202 0.366386621
203 0.581415638
204 0.342317386
205 -0.245332535
206 1.094694823
207 0.112424432
208 -0.221959158
209 0.480530188
210 -0.156565490
211 -1.076506780
212 -0.701335453
213 1.931724942
214 1.200981314
215 -0.0741596235
216 -0.111459614
217 0.110910692
218 -0.794128514
219 1.753689548
220 -0.353794949
221 -0.456119469
222 -1.000365756
223 1.249048262
224 0.0659252446
225 0.152507697
226 -0.0964857034
227 1.447406460
228 0.201667076
229 -0.304581209
230 -0.0466414493
231 0.783694906
232 0.551219877
233 0.375287586
234 -0.478718083
235 -0.171458189
236 0.944344103
237 0.0931210810
238 0.135988251
239 0.149134675
240 -0.148430896
241 1.739484351
242 1.063076582
243 -1.080905563
244 -0.297453251
245 0.385016733
246 0.514984854